Convergence of fuzzy set sequences

There are more than one mode or convergence with respect to the fuzzy set sequences. Common six modes of convergence and their relationships are discussed. These six modes are convergence in uniform metric D, convergence in separable metric Dp*, 1&lep<∞, convergence in level set, strong convergence in level set and weak convergence. Suitable counterexamples are given. The necessary and sufficient conditions of convergence in uniform metric D are described. Some comments on the convergence of LR-fuzzy number sequences are represented.